Projection effects in cluster mass estimates : the case of MS2137
Résumé
We revisit the mass properties of the lensing cluster of galaxies MS2137-23 and assess the mutual agreement between cluster mass estimates based on strong/weak lensing, X-rays and stellar dynamics. We perform a thorough elliptical lens modelling using arcs and their counter-images in the range $20\lesssim R\lesssim100$ kpc and weak lensing ($100\lesssim R\lesssim1000$ kpc). We confirm that the dark matter distribution is well consistent with an NFW profile with high concentration $c\sim11.7\pm0.6$. We analyse the consequencies of this model on the stellar kinematics of the central cD galaxy observed by \citet{sand02,sand04}. We fully calculate the line-of-sight velocity distribution (LOSVD) of stars and show that the LOSVD is not gaussian leading to $\sim 15\%$ low-biased velocity dispersion measurements close to the center. Although we quantify/correct this source of systematic uncertainty, the NFW lens model is unable to properly fit kinematical data. Furthermore our NFW model predicts a factor of $\sim2$ more massive cluster than the NFW model inferred from X-rays analysis \citep{allen01}, whereas this latter is consistent with kinematical constraints. There is a discrepancy between projected (lensing) and tridimensional (X-rays,dynamics) mass estimates. We show that such discrepancies can be explained by assuming prolate (triaxial) halos with the major axis oriented toward the line-of-sight. As well, the high concentration and the misalignement between stellar and dark matter components $(\Delta \psi \sim 13^\circ)$ support this hypothesis. We then calculate the systematic and statistical uncertainties in the relative normalization between the cylindric $M_2(